Calculus of Variations and Geometric Measure Theory

G. Di Fratta - M. Innerberger - D. Praetorius

Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics

created by difratta on 30 Apr 2021


Published Paper

Inserted: 30 apr 2021
Last Updated: 30 apr 2021

Journal: Nonlinear Analysis: Real World Applications
Volume: 55
Year: 2020

ArXiv: 1910.04630 PDF


We consider the time-dependent Landau-Lifshitz-Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time. Unlike available results in the literature, our analysis also includes the physically relevant lower-order terms like Zeeman contribution, anisotropy, stray field, and the Dzyaloshinskii-Moriya interaction (which accounts for the emergence of magnetic Skyrmions). Moreover, our proof gives a template on how to approach weak-strong uniqueness for even more complicated problems, where LLG is (nonlinearly) coupled to other (nonlinear) PDE systems.